Quantized feedback control and quantized estimation have attracted a lot of attention in recent years with many results available on both research topics. In this paper, we investigate connections between quantized feedback control and quantized estimation and try to establish a possible separation principle for quantized output feedback which would allow the control design and state estimation to become independent in a networked control environment. We also consider the use of a variable rate finite-level logarithmic quantizer and show that this may approach the minimum averaged bit rate required for quantized feedback stabilization.